- Sam and Tessa are testing a spinner to see if the probability, p , of it landing on red is less than \(\frac { 1 } { 5 }\). They both use a \(10 \%\) significance level.
Sam decides to spin the spinner 20 times and record the number of times it lands on red.
- Find the critical region for Sam's test.
- Write down the size of Sam's test.
Tessa decides to spin the spinner until it lands on red and she records the number of spins.
- Find the critical region for Tessa's test.
- Find the size of Tessa's test.
- Show that the power function for Sam's test is given by
$$( 1 - p ) ^ { 19 } ( 1 + 19 p )$$
- Find the power function for Tessa's test.
- With reference to parts (b), (d) and (e), state, giving your reasons, whether you would recommend Sam's test or Tessa's test when \(\mathrm { p } = 0.15\)